Mesoscopic correlations in Tb2Ti2O7 spin liquid

We have studied the spin correlations with $bf{k}$= ($frac12$, $frac12$, $frac12$) propagation vector which appear below 0.4, K in tbti spin liquid by combining powder neutron diffraction and specific heat on Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ samples with $x$=0, 0.01, -0.01. The $bf{k}$= ($frac12$, $frac12$, $frac12$) order clearly appears on all neutron patterns by subtracting a pattern at 1.2(1),K. Refining the subtracted patterns at 0.07,K yields two possible spin structures, with spin-ice-like and monopole-like correlations respectively. Mesoscopic correlations involve Tb moments of 1 to 2 mub ordered on a length scale of about 20 AA. In addition, long range order involving a small spin component of 0.1 to 0.2 mub is detected for the $x$= 0 and 0.01 samples showing a peak in the specific heat. Comparison with previous single crystals data suggests that the ($frac12$, $frac12$, $frac12$) order settles in through nanometric spin textures with dominant spin ice character and correlated orientations, analogous to nanomagnetic twins.